NDA2011MathematicsIndefinite IntegrationActual
What is e^x ( x + 1 2 x ) d x equal to? Where c is a constant of integration.
Options
- Ax e^x+c
- Be^x( x )+c
- C2 e^x( x )+c
- D2 x e^x+c
Correct answer
B. e^x( x )+c
Step-by-step solution
aligned & e^x ( x + 1 2 x ) d x= e^x x d x+ e^x 2 x d x & = x e^x d x- (d / d x x( x ) e^x d x ) d x+ e^x 2 x d x & =e^x x - 1 2 x e^x d x+ e^x 2 x d x & =e^x x +c aligned